version 1.6, 2010/08/13 21:04:04
|
version 1.12, 2012/12/14 14:22:46
|
Line 1
|
Line 1
|
|
*> \brief <b> ZGGEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices</b> |
|
* |
|
* =========== DOCUMENTATION =========== |
|
* |
|
* Online html documentation available at |
|
* http://www.netlib.org/lapack/explore-html/ |
|
* |
|
*> \htmlonly |
|
*> Download ZGGEV + dependencies |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zggev.f"> |
|
*> [TGZ]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zggev.f"> |
|
*> [ZIP]</a> |
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zggev.f"> |
|
*> [TXT]</a> |
|
*> \endhtmlonly |
|
* |
|
* Definition: |
|
* =========== |
|
* |
|
* SUBROUTINE ZGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, |
|
* VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO ) |
|
* |
|
* .. Scalar Arguments .. |
|
* CHARACTER JOBVL, JOBVR |
|
* INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N |
|
* .. |
|
* .. Array Arguments .. |
|
* DOUBLE PRECISION RWORK( * ) |
|
* COMPLEX*16 A( LDA, * ), ALPHA( * ), B( LDB, * ), |
|
* $ BETA( * ), VL( LDVL, * ), VR( LDVR, * ), |
|
* $ WORK( * ) |
|
* .. |
|
* |
|
* |
|
*> \par Purpose: |
|
* ============= |
|
*> |
|
*> \verbatim |
|
*> |
|
*> ZGGEV computes for a pair of N-by-N complex nonsymmetric matrices |
|
*> (A,B), the generalized eigenvalues, and optionally, the left and/or |
|
*> right generalized eigenvectors. |
|
*> |
|
*> A generalized eigenvalue for a pair of matrices (A,B) is a scalar |
|
*> lambda or a ratio alpha/beta = lambda, such that A - lambda*B is |
|
*> singular. It is usually represented as the pair (alpha,beta), as |
|
*> there is a reasonable interpretation for beta=0, and even for both |
|
*> being zero. |
|
*> |
|
*> The right generalized eigenvector v(j) corresponding to the |
|
*> generalized eigenvalue lambda(j) of (A,B) satisfies |
|
*> |
|
*> A * v(j) = lambda(j) * B * v(j). |
|
*> |
|
*> The left generalized eigenvector u(j) corresponding to the |
|
*> generalized eigenvalues lambda(j) of (A,B) satisfies |
|
*> |
|
*> u(j)**H * A = lambda(j) * u(j)**H * B |
|
*> |
|
*> where u(j)**H is the conjugate-transpose of u(j). |
|
*> \endverbatim |
|
* |
|
* Arguments: |
|
* ========== |
|
* |
|
*> \param[in] JOBVL |
|
*> \verbatim |
|
*> JOBVL is CHARACTER*1 |
|
*> = 'N': do not compute the left generalized eigenvectors; |
|
*> = 'V': compute the left generalized eigenvectors. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] JOBVR |
|
*> \verbatim |
|
*> JOBVR is CHARACTER*1 |
|
*> = 'N': do not compute the right generalized eigenvectors; |
|
*> = 'V': compute the right generalized eigenvectors. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] N |
|
*> \verbatim |
|
*> N is INTEGER |
|
*> The order of the matrices A, B, VL, and VR. N >= 0. |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] A |
|
*> \verbatim |
|
*> A is COMPLEX*16 array, dimension (LDA, N) |
|
*> On entry, the matrix A in the pair (A,B). |
|
*> On exit, A has been overwritten. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDA |
|
*> \verbatim |
|
*> LDA is INTEGER |
|
*> The leading dimension of A. LDA >= max(1,N). |
|
*> \endverbatim |
|
*> |
|
*> \param[in,out] B |
|
*> \verbatim |
|
*> B is COMPLEX*16 array, dimension (LDB, N) |
|
*> On entry, the matrix B in the pair (A,B). |
|
*> On exit, B has been overwritten. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDB |
|
*> \verbatim |
|
*> LDB is INTEGER |
|
*> The leading dimension of B. LDB >= max(1,N). |
|
*> \endverbatim |
|
*> |
|
*> \param[out] ALPHA |
|
*> \verbatim |
|
*> ALPHA is COMPLEX*16 array, dimension (N) |
|
*> \endverbatim |
|
*> |
|
*> \param[out] BETA |
|
*> \verbatim |
|
*> BETA is COMPLEX*16 array, dimension (N) |
|
*> On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the |
|
*> generalized eigenvalues. |
|
*> |
|
*> Note: the quotients ALPHA(j)/BETA(j) may easily over- or |
|
*> underflow, and BETA(j) may even be zero. Thus, the user |
|
*> should avoid naively computing the ratio alpha/beta. |
|
*> However, ALPHA will be always less than and usually |
|
*> comparable with norm(A) in magnitude, and BETA always less |
|
*> than and usually comparable with norm(B). |
|
*> \endverbatim |
|
*> |
|
*> \param[out] VL |
|
*> \verbatim |
|
*> VL is COMPLEX*16 array, dimension (LDVL,N) |
|
*> If JOBVL = 'V', the left generalized eigenvectors u(j) are |
|
*> stored one after another in the columns of VL, in the same |
|
*> order as their eigenvalues. |
|
*> Each eigenvector is scaled so the largest component has |
|
*> abs(real part) + abs(imag. part) = 1. |
|
*> Not referenced if JOBVL = 'N'. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDVL |
|
*> \verbatim |
|
*> LDVL is INTEGER |
|
*> The leading dimension of the matrix VL. LDVL >= 1, and |
|
*> if JOBVL = 'V', LDVL >= N. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] VR |
|
*> \verbatim |
|
*> VR is COMPLEX*16 array, dimension (LDVR,N) |
|
*> If JOBVR = 'V', the right generalized eigenvectors v(j) are |
|
*> stored one after another in the columns of VR, in the same |
|
*> order as their eigenvalues. |
|
*> Each eigenvector is scaled so the largest component has |
|
*> abs(real part) + abs(imag. part) = 1. |
|
*> Not referenced if JOBVR = 'N'. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LDVR |
|
*> \verbatim |
|
*> LDVR is INTEGER |
|
*> The leading dimension of the matrix VR. LDVR >= 1, and |
|
*> if JOBVR = 'V', LDVR >= N. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] WORK |
|
*> \verbatim |
|
*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) |
|
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
|
*> \endverbatim |
|
*> |
|
*> \param[in] LWORK |
|
*> \verbatim |
|
*> LWORK is INTEGER |
|
*> The dimension of the array WORK. LWORK >= max(1,2*N). |
|
*> For good performance, LWORK must generally be larger. |
|
*> |
|
*> If LWORK = -1, then a workspace query is assumed; the routine |
|
*> only calculates the optimal size of the WORK array, returns |
|
*> this value as the first entry of the WORK array, and no error |
|
*> message related to LWORK is issued by XERBLA. |
|
*> \endverbatim |
|
*> |
|
*> \param[out] RWORK |
|
*> \verbatim |
|
*> RWORK is DOUBLE PRECISION array, dimension (8*N) |
|
*> \endverbatim |
|
*> |
|
*> \param[out] INFO |
|
*> \verbatim |
|
*> INFO is INTEGER |
|
*> = 0: successful exit |
|
*> < 0: if INFO = -i, the i-th argument had an illegal value. |
|
*> =1,...,N: |
|
*> The QZ iteration failed. No eigenvectors have been |
|
*> calculated, but ALPHA(j) and BETA(j) should be |
|
*> correct for j=INFO+1,...,N. |
|
*> > N: =N+1: other then QZ iteration failed in DHGEQZ, |
|
*> =N+2: error return from DTGEVC. |
|
*> \endverbatim |
|
* |
|
* Authors: |
|
* ======== |
|
* |
|
*> \author Univ. of Tennessee |
|
*> \author Univ. of California Berkeley |
|
*> \author Univ. of Colorado Denver |
|
*> \author NAG Ltd. |
|
* |
|
*> \date April 2012 |
|
* |
|
*> \ingroup complex16GEeigen |
|
* |
|
* ===================================================================== |
SUBROUTINE ZGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, |
SUBROUTINE ZGGEV( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, |
$ VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO ) |
$ VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine (version 3.4.1) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* April 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER JOBVL, JOBVR |
CHARACTER JOBVL, JOBVR |
Line 17
|
Line 233
|
$ WORK( * ) |
$ WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* ZGGEV computes for a pair of N-by-N complex nonsymmetric matrices |
|
* (A,B), the generalized eigenvalues, and optionally, the left and/or |
|
* right generalized eigenvectors. |
|
* |
|
* A generalized eigenvalue for a pair of matrices (A,B) is a scalar |
|
* lambda or a ratio alpha/beta = lambda, such that A - lambda*B is |
|
* singular. It is usually represented as the pair (alpha,beta), as |
|
* there is a reasonable interpretation for beta=0, and even for both |
|
* being zero. |
|
* |
|
* The right generalized eigenvector v(j) corresponding to the |
|
* generalized eigenvalue lambda(j) of (A,B) satisfies |
|
* |
|
* A * v(j) = lambda(j) * B * v(j). |
|
* |
|
* The left generalized eigenvector u(j) corresponding to the |
|
* generalized eigenvalues lambda(j) of (A,B) satisfies |
|
* |
|
* u(j)**H * A = lambda(j) * u(j)**H * B |
|
* |
|
* where u(j)**H is the conjugate-transpose of u(j). |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* JOBVL (input) CHARACTER*1 |
|
* = 'N': do not compute the left generalized eigenvectors; |
|
* = 'V': compute the left generalized eigenvectors. |
|
* |
|
* JOBVR (input) CHARACTER*1 |
|
* = 'N': do not compute the right generalized eigenvectors; |
|
* = 'V': compute the right generalized eigenvectors. |
|
* |
|
* N (input) INTEGER |
|
* The order of the matrices A, B, VL, and VR. N >= 0. |
|
* |
|
* A (input/output) COMPLEX*16 array, dimension (LDA, N) |
|
* On entry, the matrix A in the pair (A,B). |
|
* On exit, A has been overwritten. |
|
* |
|
* LDA (input) INTEGER |
|
* The leading dimension of A. LDA >= max(1,N). |
|
* |
|
* B (input/output) COMPLEX*16 array, dimension (LDB, N) |
|
* On entry, the matrix B in the pair (A,B). |
|
* On exit, B has been overwritten. |
|
* |
|
* LDB (input) INTEGER |
|
* The leading dimension of B. LDB >= max(1,N). |
|
* |
|
* ALPHA (output) COMPLEX*16 array, dimension (N) |
|
* BETA (output) COMPLEX*16 array, dimension (N) |
|
* On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the |
|
* generalized eigenvalues. |
|
* |
|
* Note: the quotients ALPHA(j)/BETA(j) may easily over- or |
|
* underflow, and BETA(j) may even be zero. Thus, the user |
|
* should avoid naively computing the ratio alpha/beta. |
|
* However, ALPHA will be always less than and usually |
|
* comparable with norm(A) in magnitude, and BETA always less |
|
* than and usually comparable with norm(B). |
|
* |
|
* VL (output) COMPLEX*16 array, dimension (LDVL,N) |
|
* If JOBVL = 'V', the left generalized eigenvectors u(j) are |
|
* stored one after another in the columns of VL, in the same |
|
* order as their eigenvalues. |
|
* Each eigenvector is scaled so the largest component has |
|
* abs(real part) + abs(imag. part) = 1. |
|
* Not referenced if JOBVL = 'N'. |
|
* |
|
* LDVL (input) INTEGER |
|
* The leading dimension of the matrix VL. LDVL >= 1, and |
|
* if JOBVL = 'V', LDVL >= N. |
|
* |
|
* VR (output) COMPLEX*16 array, dimension (LDVR,N) |
|
* If JOBVR = 'V', the right generalized eigenvectors v(j) are |
|
* stored one after another in the columns of VR, in the same |
|
* order as their eigenvalues. |
|
* Each eigenvector is scaled so the largest component has |
|
* abs(real part) + abs(imag. part) = 1. |
|
* Not referenced if JOBVR = 'N'. |
|
* |
|
* LDVR (input) INTEGER |
|
* The leading dimension of the matrix VR. LDVR >= 1, and |
|
* if JOBVR = 'V', LDVR >= N. |
|
* |
|
* WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) |
|
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
|
* |
|
* LWORK (input) INTEGER |
|
* The dimension of the array WORK. LWORK >= max(1,2*N). |
|
* For good performance, LWORK must generally be larger. |
|
* |
|
* If LWORK = -1, then a workspace query is assumed; the routine |
|
* only calculates the optimal size of the WORK array, returns |
|
* this value as the first entry of the WORK array, and no error |
|
* message related to LWORK is issued by XERBLA. |
|
* |
|
* RWORK (workspace/output) DOUBLE PRECISION array, dimension (8*N) |
|
* |
|
* INFO (output) INTEGER |
|
* = 0: successful exit |
|
* < 0: if INFO = -i, the i-th argument had an illegal value. |
|
* =1,...,N: |
|
* The QZ iteration failed. No eigenvectors have been |
|
* calculated, but ALPHA(j) and BETA(j) should be |
|
* correct for j=INFO+1,...,N. |
|
* > N: =N+1: other then QZ iteration failed in DHGEQZ, |
|
* =N+2: error return from DTGEVC. |
|
* |
|
* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
Line 439
|
Line 542
|
* |
* |
* Undo scaling if necessary |
* Undo scaling if necessary |
* |
* |
|
70 CONTINUE |
|
* |
IF( ILASCL ) |
IF( ILASCL ) |
$ CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR ) |
$ CALL ZLASCL( 'G', 0, 0, ANRMTO, ANRM, N, 1, ALPHA, N, IERR ) |
* |
* |
IF( ILBSCL ) |
IF( ILBSCL ) |
$ CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR ) |
$ CALL ZLASCL( 'G', 0, 0, BNRMTO, BNRM, N, 1, BETA, N, IERR ) |
* |
* |
70 CONTINUE |
|
WORK( 1 ) = LWKOPT |
WORK( 1 ) = LWKOPT |
* |
|
RETURN |
RETURN |
* |
* |
* End of ZGGEV |
* End of ZGGEV |